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As one of the largest civil engineering systems in China, the network of high-speed railway expanded fast in the last decade. The safety of railway operation is of great concern for the whole country. Railway track irregularity is a potential threat to safety of operation and comfort of passengers, and remains a challenging issue for researchers and engineers. Currently, track irregularity data are recorded by various sensors in the comprehensive inspection cars in China. To reveal relations between the operation of high-speed trains and the track geometry, the data mining and random modeling of track irregularity are needed. In this paper, different methods to evaluate the track irregularities are presented at first. A case study of a section in Beijing-Guangzhou high-speed railway is studied using the Karhunen-Loève expansion. Track geometries that are a representation of this railway network are generated along with statistical and frequency validations. As an application based on generated random track geometries, accelerations of train body under different traveling velocities are calculated and analyzed using a simulation model. [ABSTRACT FROM AUTHOR]